Quotient Rule Proof Question

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#1
Show that if the curve y = f(x) has a maximum stationary point at x=a, then the curve y=1/f(x) has a minimum point at x=a as long as f(a) is not equal to 0:

f'(x)=0 -> f'(a)=0

y = 1/f(x) = u/v, where u = 1, v = f(x)

dy/dx = -f(x)/[f(x)]^2=0

-f(x)=0
f(x)=0

?????
0
1 year ago
#2
In order to determine whether a stationary point (f'(x) = 0 ) is a local minimum or maximum, you need to take the second derivative, f''(x). If f''(x) > 0 it's a local minimum, if f''(x) < 0 it's a local maximum.
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1 year ago
#3
(Original post by Harry-Pikesley)
dy/dx = -f(x)/[f(x)]^2=0

-f(x)=0
f(x)=0
You've not applied the quotient rule correctly.
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#4
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